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Download This PDF File A statistical insight to penalty shoot-outs in the FIFA World Cup tournaments Olly Barnes and Thai Ling April 2020 Abstract Penalty shoot-outs are used to decide the outcome of some very important football matches in the past and present. Throughout the paper, statistics will Be analysed from previous World Cup penalty shoot-outs and it will Be determined if penalties are taken at random, or if a strategy can Be implemented to statistically increase a team’s chance of winning a penalty shoot-out. This paper will investigate and attempt to justify implementing a definitive strategy. Table of Contents Abstract ............................................................................................................................ 1 1. Introduction ............................................................................................................... 3 1.1. FIFA World Cup .............................................................................................................. 3 1.2. Competition structure .................................................................................................... 3 1.3. Golden goal rule ............................................................................................................. 4 1.4. Format of a penalty shoot-out ....................................................................................... 4 1.5. When do penalty shoot-outs take place ......................................................................... 5 2. Methodology ............................................................................................................. 5 2.1. Data collection methods ................................................................................................ 5 2.2. Hypothesis ..................................................................................................................... 5 2.3. Mathematical method and other factors ........................................................................ 6 3. Results ....................................................................................................................... 6 3.1. Tournament statistics for penalty shoot-outs ................................................................. 6 3.2. Chi-Squared test ............................................................................................................ 7 3.3. Individual penalty kicks and saves statistics ................................................................... 9 4. Conclusion ............................................................................................................... 11 1. Introduction 1.1. FIFA World Cup The FIFA World Cup is an international men’s football competition which is played every four years since 1930, with the exception of 1942 and 1946 due to the Second World War [1]. The number of teams that have participated in each tournament varies. The first tournament, hosted By Uruguay, only had 13 participating national sides. This was Because it was difficult and expensive to travel across the gloBe at the time. Very few teams could afford to travel to foreign continents, so decided not to participate. [2] 1.2. Competition structure FIFA’s current format for the World Cup, since 1998, consists of 32 national teams, competing over the course of a month, with a group stage followed By the knockout stage. The group stage features eight groups, each made up of four teams, whom compete in a round roBin style tournament (all play each other once). These matches can end either in one team winning, and the other team losing, or a draw. Each team receives 3 points for a win, 0 for a loss and 1 for a draw. The two teams with the most points in each group progress to the next stage of the tournament. If two teams have the same numBer of points, their goal difference is used to determine their final position. Table 1.1 below shows group A from the FIFA World Cup 2018. Table 1.1 GROUP A PLAYED WON LOSS DRAW GOAL DIFFERENCE POINTS (P) (W) (L) (D) (GD) (Pts) URUGUAY 3 3 0 0 5 9 RUSSIA 3 2 1 0 4 6 SAUDI ARABIA 3 1 2 0 -5 3 EGYPT 3 0 3 0 -4 0 [3] From Table 1.1, it can Be seen that Uruguay won the group with 9 points, and Russia finished runner up with 6 points. Both Uruguay and Russia, advanced to the next stage of the tournament. Meanwhile, Saudi Arabia and Egypt were eliminated. The second stage of the tournament is a straight knockout. The winner of each group plays the runner-up from another group in the round of 16. The winners of these matches progress to the quarter-finals, then the semi-final and lastly the final. If any of these matches end in a draw, another 30 minutes are played as extra time. If a winner is not decided at the end of extra time; a penalty shoot-out will take place to decide the winner of the tie. This paper will be analysing the penalty shoot-outs during the knockout stages. 1.3. Golden goal rule It is important to know that the golden goal rule was implemented for the 1998 World Cup. The rule would mean that, if a team was to score in extra time, the match would end with the winning team Being the team that scored. The golden goal rule would only be used once more in the World Cup in 2002. By 2006 it was abolished due to its negative impact. [5] 1.4. Format of a penalty shoot-out In a penalty shoot-out, the team to kick first is decided By a coin toss. Each team then takes it in turns to take a shot on goal from the penalty spot, which is located 12 yards from goal. The only opposing player allowed to defend the penalty is the goalkeeper, who must stay on the goal line when the kick is taken. The shoot-out consists of each team having a total of five shots (if required), which are to Be taken By five different players. The winner of the shoot- out, is the team with the most successfully converted penalties. An example of this can Be seen below in Table 1.2. Here, Team A has successfully converted all five penalties, But Team B has only converted four, and missed one. Therefore, Team A is the winning team. Table 1.2 1 2 3 4 5 Total Team A ✔ ✔ ✔ ✔ ✔ 5 Team B ✔ ✔ ✔ ✔ ✖ 4 The shoot-out can finish early if a team has a lead that cannot Be matched. For example, Table 1.3 shows that if Team A scores their first 3 penalties and Team B misses their first 3 penalties, the shoot-out concludes. Team A would Be declared the winner in this example. This is due to the fact that Team B cannot possiBly match Team A’s score, from the remaining two penalties. Table 1.3 1 2 3 4 5 Total Team A ✔ ✔ ✔ - - 3 Team B ✖ ✖ ✖ - - 0 If Both teams are still tied after 5 penalties each, then the shoot-out continues in a sudden death format. The winner of the shoot-out is the team to score one more penalty than the other team with the same numBer of penalties taken each. Below, Table 1.4 shows that after five penalties, Both Team A and Team B have scored four. Both teams then score and then Both miss, so the shoot-out continues. On the 8th penalty, Team A scores and Team B misses, meaning Team A is the winner. Table 1.4 1 2 3 4 5 6 7 8 Total Team A ✔ ✔ ✔ ✖ ✔ ✔ ✖ ✔ 6 Team B ✔ ✔ ✔ ✔ ✖ ✔ ✖ ✖ 5 1.5. When do penalty shoot-outs take place Penalty shoot-outs only take place in the knockout stages of the FIFA World Cup. If a winner is not decided in full time then an additional 30 minutes is played, (extra time). If extra time ends in a draw, a penalty shoot-out will take place to determine the winner. This paper only collects and analyses data from penalty shoot-outs during the knockout stages. Penalties taken in the regular 90 minutes and extra time are not processed. 2. Methodology 2.1. Data collection methods Data for this paper has Been collected from the last 11 World Cup tournaments from 1978 to 2018. In these tournaments, the same format was used, (a group stage followed By a knockout stage). However, it is important to note that the data does include a period where the golden goal rule was applied. The golden goal rule will not affect the data from penalty shoot-outs, But will affect how many matches in extra time went to a penalty shoot-out. Every team that has participated in a penalty shoot-out has Been recorded, along with their success rate. The data includes each individual penalty taken, with its direction horizontally and vertically, along with the direction of the goalkeeper’s dive. With the distance of a penalty taken from 12 yards, it is commonly Believed that goalkeepers guess which direction to dive in. This is Because they do not have enough time to react and then dive in the correct direction to save the penalty. Therefore, this paper will determine if there is a position where players should aim for to increase their chances of scoring. Or if the goalkeeper should dive in a specific direction, to increase his chance of saving the penalty. 2.2. Hypothesis The data collected on penalties taken will Be used to test the following hypothesis: Null Hypothesis �#: The direction a player chooses in a penalty shoot-out in the World Cup is random. Alternative Hypothesis �$: The direction a player chooses in a penalty shoot-out in the World Cup is not random. This paper serves as an insight to whether penalties are taken randomly or if a general analysis can Be performed to increase a player’s chance of scoring a penalty or a goalkeeper’s chance of saving a penalty. The height and direction of the penalties will Be analysed to determine if penalties are truly taken at random. 2.3. Mathematical method and other factors The hypothesis that penalties are taken at random during a shoot-out can Be assessed with a chi-squared test. A chi-squared test is a test of independence. It is a procedure for testing two categorical variables and a test for goodness-of-fit. The calculated value can Be compared to a 95% significance level which evaluates the hypotheses. If the goal is divided evenly with a 3x3 grid, then it is expected that around 1/9 of all penalties analysed will Be taken in the direction of each grid. If this is not the case, it suggests that the direction a penalty is taken is not random and that specific areas of the goal are targeted over other areas.
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